How can i solve this problem? Unfortunately i have no ideas...
Let M, N oriented manifolds, $\alpha \in \Lambda^{\text{dim}(M)}(M)$ and $\beta \in \Lambda^{\text{dim}(N)}(N)$ differential forms with compact support. Let $\pi_M: M \times N \rightarrow M $ and $\pi_N: M \times N \rightarrow N $, the natural projections. Show that
$ \displaystyle \int_{M \times N} (\pi^*_M \alpha) \wedge(\pi^*_M \beta) = \int_M ( \alpha) \int_N ( \beta) $